A polynomial approximation scheme for machine scheduling on uniform processors: Using the dual approximation approach

  • Darit S. Hochbaum
  • David B. Shmoys
Session 6 Scheduling
Part of the Lecture Notes in Computer Science book series (LNCS, volume 241)


In this paper we present a polynomial approximation scheme for the minimum makespan problem on uniform parallel processors. More specifically, the problem is to find a schedule for a set of independent jobs on a collection of machines of different speeds so that the last job to finish is completed as quickly as possible. We give a family of polynomial-time algorithms {A} such that A delivers a solution that is within a relative error of ε of the optimum. The technique employed is the dual approximation approach, where infeasible but superoptimal solutions for a related (dual) problem are converted to the desired feasible but possibly suboptimal solution.


State Vector Piece Size Unused Capacity Minimum Makespan Problem Feasible Configuration 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Darit S. Hochbaum
    • 1
  • David B. Shmoys
    • 2
  1. 1.School of Business AdministrationUniversity of CaliforniaBerkeley
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridge

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